04 STAT probability 2-INDEPENDENCE

04 STAT probability 2-INDEPENDENCE - PROBABILITY THEORY Dr....

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PROBABILITY THEORY Dr. V.R. Bencivenga Economic Statistics Economics 329 INDEPENDENCE
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2 PROBABILITY THEORY Example #10 Job interview (ORIGINAL NUMERICAL EXAMPLE) A firm hires 4% of job applicants. Only some applicants are interviewed. Of all applicants hired by the firm, 98% are interviewed. Of all applicants not hired by the firm, 1% are interviewed. You have applied to this firm, and you have just received an interview. What is the probability you will be hired? I = interviewed, H = hired. What Is P(H|I)?
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3 PROBABILITY THEORY Example #10 Job interview (ORIGINAL NUMERICAL EXAMPLE) A firm hires 4% of job applicants. Only some applicants are interviewed. Of all applicants hired by the firm, 98% are interviewed. Of all applicants not hired by the firm, 1% are interviewed. You have applied to this firm, and you have just received an interview. What is the probability you will be hired? I = interviewed, H = hired. What Is P(H|I)? P(H) = .04 => 96 . ) H P( P(I | H) = .98 ) H | P(I = .01 803 . ) 96 (. 01 . ) 04 98 . ) 04 98 . ) H ) H | P(I H)P(H) | P(I ) H ( P H) | P(I I) | P(H I is th e “related event.” Probability of I given hired = .98. Probability of I given the complement of hired = .01.
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4 PROBABILITY THEORY Example #10 Job interview (ORIGINAL NUMERICAL EXAMPLE) A firm hires 4% of job applicants. Only some applicants are interviewed. Of all applicants hired by the firm, 98% are interviewed. Of all applicants not hired by the firm, 1% are interviewed. You have applied to this firm, and you have just received an interview. What is the probability you will be hired? I = interviewed, H = hired. What Is P(H|I)? P(H) = .04 => 96 . ) H P( P(I | H) = .98 ) H | P(I = .01 803 . ) 96 (. 01 . ) 04 98 . ) 04 98 . ) H ) H | P(I H)P(H) | P(I ) H ( P H) | P(I I) | P(H By getting an interview, the probability of being hired rises from 4% to 80%! The event “getting an interview” contains information about the event “being hired!” A lot of information!
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5 PROBABILITY THEORY P(H) = .04 => 96 . ) H P( complements
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6 PROBABILITY THEORY P(H) = .04 => 96 . ) H P( P(I | H) = .98 => 02 . ) H | I I|H and H | I are complements. Given H, either I or I must occur!
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7 PROBABILITY THEORY P(H) = .04 => 96 . ) H P( P(I | H) = .98 => 02 . ) H | I ) H | P(I = .01 => 99 . ) H | I I|H and H | I are complements. Given H, either I or I must occur! H | I and H | I are complements. Given H , either I or I must occur!
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8 PROBABILITY THEORY P(H) = .04 => 96 . ) H P( P(I | H) = .98 => 02 . ) H | I ) H | P(I = .01 => 99 . ) H | I H H I interviewed hired interviewed not hired H)P(H) | P(I H) = .0392 ) H )P( H | P(I ) H P(I = .0096 .0488 I not interviewed hired not interviewed not hired .9512 I|H and H | I are complements. Given H, either I or I must occur! H | I and H | I are complements. Given H , either I or I must occur!
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9 PROBABILITY THEORY P(H) = .04 => 96 . ) H P( P(I | H) = .98 => 02 . ) H | I ) H | P(I = .01 => 99 . ) H | I H H I interviewed hired interviewed not hired H)P(H) | P(I H) = .0392 ) H )P( H | P(I ) H P(I = .0096 .0488 I not interviewed hired not interviewed not hired .9512 I|H and H | I are complements.
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04 STAT probability 2-INDEPENDENCE - PROBABILITY THEORY Dr....

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